The present invention relates to methods and apparatus for drawing a surface model, and more particularly to methods and apparatus for drawing a surface model through modelling of a target object.
In the field of computer aided design using computer graphics, it is required that a surface model be drawn three dimensionally so as to display the appearance of a target object. The surface model is a model which is formed with polygons as two dimensional elements and/or curved planes as three dimensional elements. The surface model does not have information indicative of which side thereof is inside of the target object. Taking that fact into consideration, the target object is displayed three dimensionally by generating not only plane coordinate values but also plane depth values to be displayed on a pixel basis, and by applying hidden surface removal based on the depth values.
Ordinarily, a surface model has a fairly complicated form and includes plural curved lines and curved planes. To explain concretely, when the surface model illustrated in FIG. 13-A is to be drawn, first modelling to the target object is performed as a combination of plural convex polygons as illustrated with broken lines in FIG. 13-A, second the surface model is drawn by performing hidden surface removal for each convex polygon. The surface model is accordingly drawn with realistically after the modelling is performed. But the disadvantage of remarkably lengthening the time period necessary for modelling, arises because of a remarkable increase of the number of convex polygons. In the application of computer aided design, the primitive shape of the target object is previously determined, and it is strongly demanded that the design effect be checked through changing only a partial face shape. When the conventional method is employed to satisfy the demand, modelling to the entire target object is needed even when only a partial face shape thereof is changed as illustrated in FIGS. 13-A and 13-B. Operability of modelling is remarkably lowered, accordingly.
Also, it is strongly demanded that characters, figures and the like be displayed on the outer face of the target object. When a method for defining characters, figures and the like as polygons having depth values, and for displaying the characters, figures and the like with hidden surface removal, is employed to satisfy the demand, the disadvantage arises that the characters, figures and the like are not displayed partially when depth values of the characters, figures and the like are slightly different from the depth values of the surface of the target object. To overcome the disadvantage, it is necessary to employ a method which first writes characters, figures and the like to be displayed into a mapping memory, second map the characters, figures and the like on a surface model using a texture mapping method. When a texture mapping method is employed, the disadvantage arises wherein the necessary operations become complex, because reading addresses from the mapping memory should be re-established even when only the locations of the characters, figures and the like to be displayed on the target object, are changed.
A method for simply drawing a target object having a complicated shape through performing a logical operation between primitives, a so called set operation or Boolean operation, is known as a method for drawing a solid model. For example, a target object illustrated in FIG. 14-C is obtained through a union operation based on rectangular parallelepipedons as illustrated in FIGS. 14-A and 14-B. A target object illustrated in FIG. 14-D is Obtained through a difference operation based on rectangular parallelepipedons as illustrated in FIGS. 14-A and 14-B. A target object illustrated in FIG. 14-E is obtained through an intersection operation based on rectangular parallelepipedons as illustrated in FIGS. 14-A and 14-B. However, the method cannot be applied to a surface model because a surface model has no information indicative of which side of a plane is inside of the target object.